The hypothesis is that the risk of breast cancer

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Unformatted text preview: at ﬁrst childbirth.
The hypothesis is that the risk of breast cancer increases as the
length of this time interval increases. If this theory is correct, then
an important risk factor for breast cancer is age at ﬁrst birth. An
international study was set up to test this hypothesis.
Breast-cancer cases were identiﬁed among women in selected
hospitals in the United States, Greece, Yugoslavia, Brazil, Taiwan
and Japan. Controls were chosen from women of comparable age
who were in the hospital at the same time as the cases but who
did not have breast cancer. All women were asked about their age
at ﬁrst birth.
Chapter 10: Hypothesis Testing: Categorical Data Stat 491: Biostatistics Introduction
Two-Sample Test for Binomial Proportions
McNemar’s Test
Estimation of Sample Size and Power
R × C Contingency Tables
Chi-Square Goodness-of-Fit Test
The Kappa Statistic Normal-Theory Method
Fisher’s-Exact Test Example Cont’d...
We have two independent samples here.
Let p1 be the probability that age at ﬁrst birth is ≥ 30 in case
women with at least one birth.
Let p2 be the probability that age at ﬁrst birth is ≥ 30 in
control women with at least one birth.
The hypothesis of interest is then
H0 : p1 = p2 = p vs Ha : p1 = p2 . The null hypothesis says,to be over 30 at ﬁrst birth is equally
like in the two groups.
There are two approaches:
1 2 Approximate Methods (Normal-Theory or Contingency-Table
Methods)
Fisher’s-Exact Method Chapter 10: Hypothesis Testing: Categorical Data Stat 491: Biostatistics Introduction
Two-Sample Test for Binomial Proportions
McNemar’s Test
Estimation of Sample Size and Power
R × C Contingency Tables
Chi-Square Goodness-of-Fit Test
The Kappa Statistic Normal-Theory Method
Fisher’s-Exact Test Normal-Theory Method
The best estimator of p1 − p2 is p1 − p2 , the diﬀerence in the
ˆ
ˆ
sample proportions.
The large-sample sampling distribution of p1 − p2 when H0 is
ˆ
ˆ
true is
1
1
·
(ˆ1 − p2 ) ∼ N 0, p (1 − p )( + )...
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